It has pretty common connections to the Jewish Diaspora during and after World War II. While it's not as common a usage as "the Holocaust", among many folks (especially those with a little knowledge of 20th century history), "the Diaspora" refers first to the Jewish one.

The definition I'm familiar with for Jewish Diaspora (which is corroborated by all the Google hits on the first page) is the dispersal of the Jewish people starting in the 6th century BCE. Where do you get the connection to World War II?

I wonder to what extent this is actually true, and to what extent it's a meme that's grown around (the social network called) Diaspora. I've spent a fair amount of time with people who are part of the Jewish and Zimbabwean diasporas, and I've never picked up on a "dark" vibe to the word. And, as decode points out, the Jewish diaspora refers primarily to the ancient Jewish exile and dispersal from Palestine, not to 20th century history. I see the word more as a part of Jewish culture and tradition that's if anything celebrated, but Jewish readers are welcome to tell me I'm being crass and culturally insensitive.